Acubical container of side a and wall thickness x (a: « a) is suspendedin air and filled n molesof diatomic gas (adiabatic exponent=y) inaroom where room temperature isT^. Ifat/ = 0 gastemperature is Fj (F, > Fq), find the gas temperature as a function of time t. Assume the heat is conducted through all the walls ofcontainer.
Acubical container of side a and wall thickness x (a: « a) is suspendedin air and filled n molesof diatomic gas (adiabatic exponent=y) inaroom where room temperature isT^. Ifat/ = 0 gastemperature is Fj (F, > Fq), find the gas temperature as a function of time t. Assume the heat is conducted through all the walls ofcontainer.
Text Solution
AI Generated Solution
To solve the problem, we need to find the gas temperature \( T \) as a function of time \( t \) for a cubical container filled with diatomic gas. The process involves understanding heat conduction through the walls of the container and how it affects the temperature of the gas inside.
### Step-by-step Solution:
1. **Understanding the Setup**:
- We have a cubical container with side length \( a \) and wall thickness \( x \).
- The container is filled with \( n \) moles of a diatomic gas, which has an adiabatic exponent \( \gamma = \frac{7}{5} \).
- The initial temperature of the gas at \( t = 0 \) is \( T_1 \), and the room temperature is \( T_0 \) (where \( T_1 > T_0 \)).
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Knowledge Check
Figure shows a long cylindrical container with ideal gas in two chambers. Lower chamber is filled with one mole of a mono atomic gas, while upper chamber has one mole of a diatomic gas. The gases initially are at temperature 300K , the container walls as well as pistons are conducting. Both the pistons are identical with mass 'M' and area 'A' such that (Mg)/A=P_(0) (atmosphere pressure). Assuming the ideal gas constant to be R , answer the following questions: Total work done by the ideal gases in this process is
Figure shows a long cylindrical container with ideal gas in two chambers. Lower chamber is filled with one mole of a mono atomic gas, while upper chamber has one mole of a diatomic gas. The gases initially are at temperature 300K , the container walls as well as pistons are conducting. Both the pistons are identical with mass 'M' and area 'A' such that (Mg)/A=P_(0) (atmosphere pressure). Assuming the ideal gas constant to be R , answer the following questions: Total work done by the ideal gases in this process is
A
`300Rln(3)`
B
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zero
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